Paper Info
Title
On the method of logarithmic cumulants for parametric probability density function estimation.
Abstract
Parameter estimation of probability density functions is one of the major steps in the area of statistical image and signal processing. In this paper we explore several properties and limitations of the recently proposed method of logarithmic cumulants (MoLC) parameter estimation approach which is an alternative to the classical maximum likelihood (ML) and method of moments (MoM) approaches. We derive the general sufficient condition for a strong consistency of the MoLC estimates which represents an important asymptotic property of any statistical estimator. This result enables the demonstration of the strong consistency of MoLC estimates for a selection of widely used distribution families originating from (but not restricted to) synthetic aperture radar image processing. We then derive the analytical conditions of applicability of MoLC to samples for the distribution families in our selection. Finally, we conduct various synthetic and real data experiments to assess the comparative properties, applicability and small sample performance of MoLC notably for the generalized gamma and $K$ families of distributions. Supervised image classification experiments are considered for medical ultrasound and remote-sensing SAR imagery. The obtained results suggest that MoLC is a feasible and computationally fast yet not universally applicable alternative to MoM. MoLC becomes especially useful when the direct ML approach turns out to be unfeasible.
Year
DOI
Venue
2013
10.1109/TIP.2013.2262285
IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Keywords
Field
DocType
asymptotic property,statistical image,$k$-distribution,supervised image classification,signal processing,image processing,parametric probability density function estimation,probability density function,parameter estimation,maximum likelihood estimation,molc parameter estimation,generalized gamma distribution,gamma distribution,method of moments approach,image classification,remote-sensing sar imagery,logarithmic cumulant,strong consistency,k-distribution,method of moments,medical ultrasound sar imagery,mom approach,statistical estimator
Artificial intelligence,Estimation theory,Mathematical optimization,K-distribution,Pattern recognition,Algorithm,Parametric statistics,Gamma distribution,Strong consistency,Probability density function,Mathematics,Generalized gamma distribution,Estimator
Journal
Volume
Issue
ISSN
22
10
1941-0042
Citations 
PageRank 
References 
21
1.00
15
Authors
4
Name
Order
Citations
PageRank
Vladimir A. Krylov113314.81
Gabriele Moser291976.92
Serpico, S.B.356048.52
Josiane Zerubia4492.24